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A maximum likelihood estimator for long-range persistence

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  • Guerrero, Alexandra
  • Smith, Leonard A.

Abstract

A wide variety of processes are thought to show “long-range persistence”, specifically an autocorrelation function with power-law decay. A variety of methods have been proposed to quantify this power-law decay, and weather and climate systems, among others, have been claimed to show long-range persistence. In this paper we present a new approach, defining and illustrating a new maximum likelihood estimator of the persistence exponent H. This method provides estimates of H at each time scale considered, as well as meaningful uncertainty estimates. Several independent realisations of processes with a known degree of long-range persistence are used to test the accuracy of the new estimator in terms of spread and bias. The persistence exponent of temperature data is estimated and the problems of using observational data are addressed.

Suggested Citation

  • Guerrero, Alexandra & Smith, Leonard A., 2005. "A maximum likelihood estimator for long-range persistence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 619-632.
    • Handle: RePEc:eee:phsmap:v:355:y:2005:i:2:p:619-632
    DOI: 10.1016/j.physa.2005.03.002
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    References listed on IDEAS

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    1. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    2. Plamen Ch. Ivanov & Luís A. Nunes Amaral & Ary L. Goldberger & Shlomo Havlin & Michael G. Rosenblum & Zbigniew R. Struzik & H. Eugene Stanley, 1999. "Multifractality in human heartbeat dynamics," Nature, Nature, vol. 399(6735), pages 461-465, June.
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